Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 403 · 40 questions

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

1. 1.Two angles of a triangle are 70° and 50°. What is the exterior angle at the third corner? (a) 110° (b) 130° (c) 120° (d) 60°
2. 2.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 150° (c) 120° (d) 300°
3. 3.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 120° (c) 60° (d) 121°
4. 4.Two angles of a triangle are 20° and 35°. What is the exterior angle at the third corner? (a) 160° (b) 55° (c) 125° (d) 145°
5. 5.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 10° (c) 85° (d) 5°
6. 6.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 30° (c) 150° (d) 110°
7. 7.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 15° (b) 165° (c) 195° (d) 16°
8. 8.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 250° (b) 71° (c) 70° (d) 110°
9. 9.Two angles of a triangle are 60° and 95°. What is the third angle? (a) 25° (b) 85° (c) 120° (d) 155°
10. 10.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 125° (b) 135° (c) 80° (d) 100°
11. 11.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 140° (b) 150° (c) 70° (d) 30°
12. 12.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 145° (d) 125°
13. 13.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 120° (b) 30° (c) 61° (d) 60°
14. 14.Two angles of a triangle are 75° and 65°. What is the exterior angle at the third corner? (a) 105° (b) 140° (c) 115° (d) 40°
15. 15.Two angles of a triangle are 60° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 100° (c) 140° (d) 80°
16. 16.Two angles of a triangle are 45° and 30°. What is the third angle? (a) 150° (b) 75° (c) 135° (d) 105°
17. 17.Two angles of a triangle are 55° and 30°. What is the third angle? (a) 125° (b) 150° (c) 85° (d) 95°
18. 18.Two angles of a triangle are 25° and 40°. What is the exterior angle at the third corner? (a) 155° (b) 115° (c) 65° (d) 140°
19. 19.In an isosceles triangle, the two equal angles are 55° each. What is the third angle? (a) 35° (b) 70° (c) 125° (d) 55°
20. 20.Two angles of a triangle are 45° and 20°. What is the third angle? (a) 65° (b) 160° (c) 135° (d) 115°
21. 21.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 140° (b) 160° (c) 320° (d) 20°
22. 22.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 120° (c) 130° (d) 70°
23. 23.Two angles of a triangle are 40° and 85°. What is the exterior angle at the third corner? (a) 55° (b) 95° (c) 125° (d) 140°
24. 24.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 50° (c) 40° (d) 70°
25. 25.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 70° (c) 110° (d) 160°
26. 26.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 130° (c) 105° (d) 75°
27. 27.Two angles of a triangle are 40° and 100°. What is the exterior angle at the third corner? (a) 80° (b) 40° (c) 140° (d) 220°
28. 28.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 125° (d) 55°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 230° (c) 50° (d) 115°
30. 30.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 210° (c) 150° (d) 31°
31. 31.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 121° (c) 240° (d) 60°
32. 32.Two straight lines cross. Two vertically opposite angles add up to 100°. What is each of the other two angles? (a) 80° (b) 50° (c) 260° (d) 130°
33. 33.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 35° (b) 120° (c) 95° (d) 145°
34. 34.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 140° (d) 100°
35. 35.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 155° (c) 25° (d) 26°
36. 36.Two angles of a triangle are 25° and 140°. What is the third angle? (a) 155° (b) 165° (c) 40° (d) 15°
37. 37.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 70° (c) 120° (d) 60°
38. 38.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 70° (b) 110° (c) 140° (d) 71°
39. 39.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 10° (c) 100° (d) 20°
40. 40.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 20° (c) 110° (d) 40°

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